Thanks to digital technology, methods for finding and analysing research literature have become dramatically more powerful over the last decades. Also, new bibliometric techniques have been developed and applied to the results of such literature search queries. The application of these bibliometric tools to mathematics education research, however,…

Educators often argue that students should engage in activities such as conjecturing, proving, and deductive reasoning. The underlying principle is that learning mathematics means doing as mathematicians do. However, "mathematician" implicitly refers to a pure mathematician at university. "The aim of our paper is to critically…

The value of some university mathematics courses gets characterized within a liberal arts course of study in terms of supporting "critical thinking skills" or some other phrase for generally improved reasoning. This can be seen as an application of the millennia old "Theory of Formal Discipline" that claims that mathematics…

In this document, we search for and define an infinite limit of sequences that is correct and accepted by the mathematical experts, the final purpose of which is to analyze its phenomenology, in Freudenthal's sense. To make the choice, experts were consulted on two issues. The first one was not decisive because of the effect that the divergence…

The purpose of this note is to describe several challenging problems in Euclidean geometry. The note also contains author's solution sketches to the two problems.

Within a multitiered system of support (MTSS), students who struggle to learn mathematics often receive core instruction and supplemental intervention in different settings, with different teachers and different sets of curriculum materials, all of which can result in poor alignment. This curriculum crosswalk describes how three sets of materials…

Teaching students to reason with data is not a totally new enterprise. A small but insistent statistics education community has been studying the process for decades. This commentary provides an introduction to some major themes of that research, in order to provide common ground for conversations between learning sciences researchers and those…

This paper discusses a concept that we call "'m'-tile means," which are the arithmetic mean of data values that break a data set into "m"-1 equal parts. Studying "m"-tile means can engage students' critical thinking skills and demonstrate the concepts underlying commonly used measures of central tendency, and so they…

A professional development program in Salt Lake City aims to show math teachers what it's like to be in a math class oriented around discourse and inquiry. The effort, write Meghan Everette and Benjamin Shuldiner, is helping the teachers gain a sense efficacy in this critical but underutilized area of math instruction.

Learning curves are an important tool in cognitive diagnostics modeling to help assess how well students acquire new skills, and to refine and improve knowledge component models. Learning curves are typically obtained from a model estimated on real data obtained from a finite, and usually limited, sample of students. As a consequence, there is…

This study analyses the view of students' mental models in solving mathematical problems. The study employed a literature review using well-accepted and robust guidelines. Data were collected by searching books and articles of journals. Data analysis techniques were done qualitatively. The finding of this study showed that the mental model is…

The paper discusses technology that can help students master four triangle centers -- circumcenter, incenter, orthocenter, and centroid. The technologies are a collection of web-based apps and dynamic geometry software. Through use of these technologies, multiple examples can be considered, which can lead students to generalizations about triangle…

The importance of mathematical problem posing has been acknowledged by many researchers. In this theoretical paper, we want to capture different meanings and aspects of problem posing by approaching it from three different levels: (1) by comparing definitions, (2) by relating it to other constructs, and (3) by referring to research and teaching…

Pre-service mathematics teachers (PSTs) enter university with diverse beliefs and understandings of teaching and learning; yet, they may not be aware of how these conceptions are related to their epistemological and efficacy beliefs. This study explored how the mathematical beliefs, mathematics self-efficacy, and mathematics teaching efficacy of…

In the research reported in this paper we investigated teachers' changes when adopting and adapting to emergency online teaching during the COVID-19 pandemic, from the perspective of the Interconnected Model of Professional Growth (IMPG). By adapting complementary accounts methodology to research into teachers' changes when addressing the…